In a Young's double slit experiment the slit are 0.2 mm apart and the screen is 1.5 m away.It is observed that the distance between the central brigth fringe and fourth dark fringe is 1.8 cm .Find the wavelength of light used.

Explanation

`d = 0.4 mm = 0.4 xx 10^(-3) m = 4 xx 10^(-4) m`
`D = 1.6 m`
For dark fringes,
`y_(m) =(m + 1/2) (lambdaD)/d`
For fourth dark fringe,
m = 3
`therefore y_(3) = (3+1/2) (lambda xx 1.6)/(4 xx 10^(-4))`
But, `y_(3) = 1.7 cm = 1.7 xx 10^(-2) m`
`rArr (16 lambda (7/2))/(4 xx 10^(-4)) = 1.7 xx 10^(-2) = 1.21 xx 10^(-6) `
`lambda = 1.21 mu m`